# The general solution of a first order differential polynomial

## Michael Singer

### North Carolina State University

This is the title of a 1976 paper by Richard Cohn in which he gives a purely algebraic proof of a theorem (proved analytically by Ritt) that gives a bound on the number of derivatives needed to find a basis for the radical ideal of the general solution of such a polynomial. I will show that the method introduced by Cohn can be used to give a modern proof of a theorem of Hamburger stating that a singular solution of such a polynomial is either an envelope of a set of solutions or embedded in an analytic family of solutions depending on whether or not it corresponds to an essential singular component of this polynomial. I will also discuss the relation between this phenomenon and the Low Power Theorem. This will be an elementary talk with all these terms and concepts defined and explained.

Michael Singer is a professor at North Carolina State University, studying differential algebra, difference algebra, and symbolic computation. He received his Ph.D. in 1974 from the University of California at Berkeley, under the supervision of Maxwell Rosenlicht.